A simple method to do circular convolution

This describes a simple method I found to do circular convolution, which I think is simpler than the method
I saw in Digital Signal Processing, by Proakis, Manolakis.

This is a method to compute the circular convolution for points between two sequences, where is
the length of the longer of the two sequences (or the length of the sequences if they are of equal
length).

Let the ﬁrst sequence and the second sequence , where the square
around the number indicates the time .

We want to ﬁnd where is circular convolution.

The process requires as many steps as there are entries in the longer sequence .

The process to to ﬁnd is illustrated using a diagram. The ﬁrst step is to pad the smaller
sequence by zeros so that it is the same length as the longer sequence. The method is explained in the
diagrams

Now is found using the same process as above, but is moved to the right by position instead of
zero positions.

Notice that in the above step, we see that the origin (index ) of sequence happened to be aligned
with the origin of the sequence , this means that is the origin of the since this is the index for
being generated in this step.

Now is found using the same process as above, but is moved to the right by positions.

Now is found using the same process as above, but is moved to the right by positions.

Now is found using the same process as above, but is moved to the right by positions.